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Groups and FieldsChallengeThe Sylow Theorems

The Sylow Theorems · Challenge problem

In a group of order 105105, suppose n5=21n_5=21 (the Sylow 55-subgroups are not normal) and n7=15n_7=15 (the Sylow 77-subgroups are not normal). How many elements of order 55 or order 77 would this force GG to have in total?